Abstract
A non-stationary Gaussian random field model is developed based on a combination of the SPDE approach and the classical deformation method. With the deformation method, a stationary field is defined on a domain which is deformed so that the field is non-stationary on the new domain. We show that if the stationary field is a Mat´ern field defined as a solution to a fractional SPDE, the resulting non-stationary model can be represented as the solution to another fractional SPDE on the deformed domain. By defining the model in this way, the computational advantages of the SPDE approach can be combined with the deformation method’s more intuitive parameterisation of non-stationarity. In particular it allows for essentially independent control over the non-stationary practical correlation range on one hand and the variance on the other hand. This has not been possible with previously proposed non-stationary SPDE models.
The model is tested on spatial data of significant wave height, a characteristic of ocean surface conditions which is important when estimating the wear and risks associated with a planned journey of a ship. The model is fitted to data from the north Atlantic and is used to compute wave height exceedance probabilities and the distribution of accumulated fatigue damage for ships traveling a popular shipping route. The model results agree well with the data, indicating that the model could be used for route optimization in naval logistics.
Brief Biography
David Bolin is an associate professor of statistics in the CEMSE Division at KAUST. Prior to joining KAUST, he was an associate professor in mathematical statistics at the University of Gothenburg. His main research interests are in stochastic partial differential equations and their applications in statistics, with a focus on development of practical, computationally efficient tools for modelling non-stationary and non-Gaussian processes.